Limit Theorems for Trawl Processes

Abstract

In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{i{\Delta }_n}{)}_{i=0}^{\lfloor nt\rfloor -1}$, under the assumption that as $n\uparrow \infty$, ${\Delta }_n\downarrow 0$ and $n{\Delta }_n\to \mu \in [0,+\infty ]$. Second, we derive a functional limit theorem for trawl processes as the Lévy measure of the trawl seed grows to infinity and show that the limiting process has a Gaussian moving average representation.

35 pages

References in corpus (2)

• Continuous time analysis of fleeting discrete price moves
• Likelihood inference for exponential-trawl processes